Nature of the repulsive Coulomb barrier in multiply charged negative ions

Abstract

The repulsive Coulomb barrier (RCB) for electron emission is a general property of multiply charged anions. When an electron is emitted from a multiply charged anion, the electron experiences short-range attraction by the nuclei and long-range repulsion from the remaining negatively charged system, giving rise to the RCB. Although the RCB is dominated by the electrostatic forces present, it is argued that the exact potential the electron experiences is nonlocal and energy dependent. The theory of the RCB is outlined and related to the theory of Green's functions. Since it is complicated to compute a nonlocal and energy-dependent potential, approximation schemes are introduced that allow convenient calculation of local energy-independent RCB potentials. Three approximation schemes of complementary nature are proposed. The physical meaning of these schemes, the underlying approximations, and their possible weaknesses are discussed in detail. The local approximation schemes are used to calculate the RCB of atomic dianions ${\mathrm{F}}^{2\mathrm{\ensuremath{-}}}$ and ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ and of the linear carbon cluster dianions ${\mathrm{C}}_{n}^{2\ensuremath{-}}$ $(n=2,4,6,8).$ The atomic dianions serve as convenient objects to study the basis-set dependence of the local approximation schemes. The computed local potentials of the carbon dianions are used to calculate their lifetimes in the framework of Wentzel-Kramer-Brillouin theory. We found that the lifetime of the linear carbon dianions grows markedly when going from ${\mathrm{C}}_{2}^{2\mathrm{\ensuremath{-}}}$ to ${\mathrm{C}}_{8}^{2\mathrm{\ensuremath{-}}},$ and that the latter should be the only species observable in a mass spectrometer. This agrees with the available experimental findings.